what is the answer to the equation 3/5x+2=5.6
Answers
Let the given equation is
\(\begin{gathered} \frac{3}{5}x+2=5.6 \\ \frac{3}{5}x=5.6-2 \\ \frac{3}{5}x=3.6 \\ x=3.6\times\frac{5}{3} \\ x=\frac{18}{3} \\ x=6 \end{gathered}\)Hence the value of x is 6.
Related Questions
Question 3 of 56
Triangle ABC has vertex coordinates A(-5, 2), B(-1, 3), and C(-1, 1). It is
rotated 90° clockwise around the origin. What are the coordinates of C?
Answers
Answer:1,1
Step-by-step explanation:if you do it 90 degrees all the way around ur gonna get 1,1.
Answer:
The coordinates of A' are (-1,-3) , B' are (-2,-2) , C' are (-4,-3).
Step-by-step explanation:
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
Answers
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
What do you mean by compound?A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.
Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.
We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:
3 ml x 3 ml x 3 ml
-------- = ----------
728 ml total, 8 ml overall
If we cross-multiply, we obtain:
8(x) = 3(728)
To find x, we use the formula x = 3(728)/8 = 273
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
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273 milliliters of compound A are needed to make 728 milliliters of the drug.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.
Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:
3 : (3+5) or 3:8
This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.
To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:
3/8 = x/728
where x represents the amount of compound A needed.
To solve for x, we can cross-multiply:
8x = 3*728
8x = 2184
x = 273
Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.
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How to illistrate 1/3×1/2
Answers
Answer:
=1/6
Step-by-step explanation:
thats the answer
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Can you please tell me a with this question I am reviewing for a final
Answers
Since the function of the difference between the length of spring and non-compressed length is
\(f(\theta)=2cos\theta+\sqrt{3}\)Part A:
If the two lengths are equal then the difference will be 0, then equate f(theta) by 0
\(\theta\rightarrow theta\)\(\begin{gathered} f(\theta)=0 \\ 2cos\theta+\sqrt{3}=0 \end{gathered}\)Subtract root 3 from both sides
\(\begin{gathered} 2cos\theta+\sqrt{3}-\sqrt{3}=0-\sqrt{3} \\ 2cos\theta=-\sqrt{3} \end{gathered}\)Divide both sides by 2
\(\begin{gathered} \frac{2cos\theta}{2}=-\frac{\sqrt{3}}{2} \\ cos\theta=-\frac{\sqrt{3}}{2} \end{gathered}\)Since the values of cos are negative in the 2nd and 3rd quadrant, then we will find the value of theta on them
\(\begin{gathered} \theta=\pi-cos^{-1}(\frac{\sqrt{3}}{2}) \\ \theta=\pi-\frac{\pi}{6}+2\pi n \\ \theta=\frac{5\pi}{6}+2\pi n \end{gathered}\)\(\begin{gathered} \theta=\pi+\frac{\pi}{6}+2\pi n \\ \theta=\frac{7\pi}{6}+2\pi n \end{gathered}\)n is any integers
Part B:
We will replace theta with 2 theta
\(\begin{gathered} 2\theta=\pi-(cos^{-1}\frac{\sqrt{3}}{2}) \\ 2\theta=\pi-\frac{\pi}{6} \\ 2\theta=\frac{5}{6}\pi \\ \frac{2\theta}{2}=\frac{\frac{5\pi}{6}}{2} \\ \theta=\frac{5\pi}{12} \end{gathered}\)\(\begin{gathered} 2\theta=\pi+cos^{-1}(\frac{\sqrt{3}}{2}) \\ 2\theta=\pi+\frac{\pi}{6} \\ 2\theta=\frac{7\pi}{6} \\ \frac{2\theta}{2}=\frac{\frac{7\pi}{6}}{2} \\ \theta=\frac{7\pi}{12} \end{gathered}\)n = 1 because the interval from [0, 2pi]
Then the value of theta in part 2 is half the value of theta in part 1
The function with 2theta is
\(f(2\theta)=2cos2\theta+\sqrt{3}\)Part C:
The other given equation is
\(g(x)=1-sin^2\theta+\sqrt{3}\)We will equate the two functions to find the time
\(\begin{gathered} f(\theta)=g(\theta) \\ 2cos\theta+\sqrt{3}=1-sin^2\theta+\sqrt{3} \end{gathered}\)Subtract root 3 from both sides
\(\begin{gathered} 2cos\theta+\sqrt{3}-\sqrt{3}=1-sin^2\theta+\sqrt{3}-\sqrt{3} \\ 2cos\theta=1-sin^2\theta \end{gathered}\)Since
\(1-sin^2\theta=cos^2\theta\)Then
\(2cos\theta=cos^2\theta\)Subtract 2cos theta from both sides
\(\begin{gathered} 2cos\theta-2cos\theta=cos^2\theta-2cos\theta \\ 0=cos^2\theta-2cos\theta \end{gathered}\)Take cos theta as a common factor
\(\begin{gathered} cos\theta(\frac{cos^2\theta}{cos\theta}-\frac{2cos\theta}{cos\theta})=0 \\ cos\theta(cos\theta-2)=0 \end{gathered}\)Equate each factor by 0 to find the value of theta
\(\begin{gathered} cos\theta=0 \\ \theta=0,\theta=\pi \end{gathered}\)\(\begin{gathered} cos\theta-2=0 \\ cos\theta-2+2=0+2 \\ cos\theta=2\rightarrow neglect\text{ it because 0}\leq cos\theta\leq1 \end{gathered}\)Then they have the same length at the time
\(\theta=0,\theta=\pi\)Please help me I’m stuck on this.
Oliver wants to play the gone fishing game at the carnival.He will use the graph to find the total cost (Y) to play a couple of games.If Oliver wants to play 4 games,how much will he pay?
If u need more information tell me in the comments :)
Answers
Answer:
The cost of the game is $7 .
Step-by-step explanation:
By looking at the graph, the line at x = 4 is equals to y = 7
One winter day, the temperature ranged from a high of 20 degrees to a low of -25 degrees. By how many degrees did the temperature change?
Answers
Answer:
+20° to -25° = 45° C/F temperature change
Step-by-step explanation:
in an experiment to learn whether substance m can help restore memory, the brains of 20 rats were treated to damage their memories. first, the rats were trained to run a maze. after a day, 10 rats (determined at random) were given substance m and 7 of them succeeded in the maze. only 2 of the 10 control rats were successful. the two-sample z test for the difference in the true proportions. Gives z= 2.25, P< 0.02
Answers
The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.
This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).
In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.
Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
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True or False: The Sine Function, y=sin(2), has a Horizontal Asymptote.
True
O False
Answers
Answer:
true
Step-by-step explanation:
5
Which fraction is equivalent to 20
?
N
Answers
Answer:
4/20
Step-by-step explanation:
Select the correct answer.
It costs $480.00 to rent an apartment on the Gold Coast for a weekend. Last year it cost $400.00.
What method below shows how you would calculate the % increase?
Answers
The method is: Find the increase and find the ratio of the increase and the old price.
The percentage increase is 20%
What method below shows how you would calculate the percentage increase?A percentage is defined as the ratio that can be expressed as a fraction of 100.
The method below shows how you would calculate the % increase.
First step: Find the increase:
increase = 480 - 400 = $80
Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:
80/400 * 100 = 20%
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Any help with this question will be much appreciated! Thanks
Answers
a) The range is the set of all values of y that satisfies the function. On the graph, it is between the highest value of y on the graph and the lowest value of y on the graph. Looking at the graph,
minimum point = - ∞
maximum point = 4
Range = (- ∞, 4]
b) The domain is the set of all values of x that satisfies the function. On the graph, it is between the highest value of x on the lft graph and the lowest value of x on the graph. Looking at the graph,
minimum point = - ∞
maximum point = 6
Domain = (- ∞, 6]
c) f(- 2) = 4
d) f(x) = 0 at x = - 4 and x = 0
e) The intervals on which f(x) is decreasing is
From x = - 2 to x = 0
f) The minimum is the lowest point on the graph. Thus, there is a relative minimum at
x = 0
ach ant has 6 legs. How many legs do 3 ants have?
Ants 1 2 3
Legs 6 ?
Answers
Answer:
Step-by-step explanation:
the answer is 18 I think?
Answer:
18
Step-by-step explanation:
6 (legs) x 3 (ants) = 18 legs
It can also be represented as 6+6+6 (18)
hope this helps :)
Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 29, 31, 49, 37, 26, 28. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
Answers
The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.
Step 1: Set up hypotheses
H₀: The outcomes of the die are equally likely.
H₁: The outcomes of the die are not equally likely.
Step 2: Select the significance level
The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.
Step 3: Compute the test statistic
We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.
Expected frequencies (fair die):
1: 200/6 = 33.33
2: 200/6 = 33.33
3: 200/6 = 33.33
4: 200/6 = 33.33
5: 200/6 = 33.33
6: 200/6 = 33.33
Applying the chi-square formula, we get the test statistic:
χ² = ∑((observed - expected)² / expected)
Calculating this value, we get χ² ≈ 13.97.
Step 4: Determine the critical value
Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.
Step 5: Make a decision
The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.
The loaded die appears to behave differently from a fair die.
In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
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12 Sam is wondering if there is a pattern that he can use to divide the whole number 3 by powers of 10. Part A Write a whole number. Then write a decimal equivalent to the whole number with zero tenths and hundredths.
Answers
The pattern can be written as a whole number by the general equation written as, \(E = \dfrac{n} { 10^k }\).
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Decimal equivalent to 12 with zero tenths and hundredths: 12.00
To divide 3 by powers of 10, we can simply move the decimal point to the left by the same number of places as the exponent of 10. For example:
3 ÷ 10 = 0.3
3 ÷ 100 = 0.03
3 ÷ 1000 = 0.003
and so on.
So in general, to divide a whole number n by a power of 10 with exponent k, we can write:
The pattern can be written as:-
\(E = \dfrac{n} { 10^k }\)
Then we can move the decimal point in the numerator k places to the left to get the decimal equivalent.
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a number,x, rounded to 1 significant figure is 40 write down the error interval for x
Answers
Answer:
Error interval is \(35\leq x< 45\)
Step-by-step explanation:
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
Solution:
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is \(35\leq x< 45\).
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
Among all pairs of numbers whose difference is 16, find the pair whose product
is minimum. What is the minimum product
Answers
Answer:
-8 and 8.
Product is -64.
Step-by-step explanation:
Let the numbers be x and x + 16.
We need to find the minimum of x(x + 16).
Product P = x^2 + 16x.
Convert to vertex form:
P = (x + 8)^2 - 64
The minimum value of (x + 8)^2 = 0 so:
The minimum of this is when x = -8 ,giving P = -64.
The pair of numbers is -8 and -8+16 = 8
and the minimum product = -46.
The pair whose product is minimum is; -8 and 8.
The two numbers whose difference is 16 can be represented as;
x and (x+16)The product of the numbers can be represented as Product, P as follows;
P = x(x +16)P = x² +16xBy completing the square technique;
P = (x + 8)² -64.In other words;
The minimum value of (x + 8)² should be equal to 0.
(x+8)² = 0
Hence, the minimum of this is when x = -8.
The pair of numbers is then;
x = -8 and (x+16) = -8 +16 = 8Ultimately, the minimum product is: -8 × 8 = -64.
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rewrite the fractions 3/4 and 7/10 as fractions with a least common denominator. a. 15/20 and 14/20b. 60/80 and 56/80c. 30/40 and 28/40d. 3/20 and 7/20
Answers
The rewritten fractions are 15/20 and 14/20. The correct answer is (a) 15/20 and 14/20.
To rewrite the fractions 3/4 and 7/10 with a least common denominator, follow these steps:
1. Find the least common multiple (LCM) of the denominators 4 and 10.
The LCM is the smallest number that both denominators can divide into.
In this case, the LCM is 20.
2. Rewrite each fraction with the new denominator (20) by multiplying the numerator and the denominator of each fraction by the necessary factor to reach the LCM.
For 3/4:
(3 * 5)/(4 * 5) = 15/20
For 7/10:
(7 * 2)/(10 * 2) = 14/20.
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On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes through (2, 0).
Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Select two options.
The domain of the function is the set of all values x such that x is greater than or equal to one-quarter.
The range of the function is all real numbers.
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
The function is increasing over the interval (negative 6 and one-eighth, ∞).
Answers
The statements true about the the function f(x) = 2x2 – x – 6 are-
The vertex of the function is (one-quarter, negative 6 and one-eighth).The function has two x-intercepts.What is vertex of parabola?The vertex of parabola is the point at the intersection of parabola and its line of symmetry.
Now the given function is,
f(x) = 2x^2 – x – 6
Also, it is given that the vertex is located at (0.25, -6) and the parabola opens up, the function has two x-intercepts.
Comparing the given function with standard form,
f(x) = a x^2 bx + c
By comprison we get,
a = 2
b = -1
c = -6
Now, x-coordinate of vertex is given as,
x = -b/2a
put the values we get,
x = -(-1)/2*2
or, x = 1/4
Put the value of x in given function, so y-coordinate of the vertex is given as,
f(1/4) = 2(1/4)² - 1/4 - 6
= -49/6
= -6 1/8
Hence, The statements true about the the function f(x) = 2x2 – x – 6 are-
The vertex of the function is (one-quarter, negative 6 and one-eighth).The function has two x-intercepts.More about vertex :
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Answer:
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
Step-by-step explanation:
The answer above is correct.
What is the domain and range of each relation
Answers
Answer:
1 ans
domain=(-2,0,2,4)
range=(-3,-1,0)
2 ans
domain=(-3,-1,0,3)
range=(-1,0,1,2,3)
Step-by-step explanation:
A study of 100 recent high school graduates
investigates a link between their childhood reading
habits and achievement in high school.
10
Participants are asked if they read books every night
with another person when they were ages 2 to 5, as
well as their grade average for all of their high school
classes. The results are represented in the table
What does the 21 in the table represent?
Answers
The number 21 refers to the number of people out of 100 who used to read books every night and obtained a B in their classes.
What does the chart show?This chart shows the number of people, their grades and whether they used to read books.
Number of people: This is expressed by the numbers. If you add all the numbers the total is 100 (total of people interviewed).People who read books nightly vs people who didn't: The columns classify people based on this category.Average grade: The rows show the average grade.What does 21 mean?The number 21 is aligned with the column read books nightly and the row B average. This means this number implies that 21 out of the 100 people read books nightly and obtained a B in their classes.
Note: This question is incomplete because the chart is not provided. Below, I attached the figure.
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4. In AABC below, ZASZC.BAсWhich sentence validates the statement AB = CB?
Answers
From the figure in the question;
\(\angle A\text{ }\cong\angle C\)Since these angles are equal
then
If two angles of a triangle are congruent then the sides opposite the angles are congruent
Hence
\(\vec{AB}\text{ = }\bar{\text{CB}}\)Thus,
If two angles of a triangle are congruent then the sides opposite the angles are congruent is sufficient to prove that AB = CB
which of these health care plans do federal and state governments offer?
Answers
2.93 km
Before the eruption of a volcano, the volcano was 2.93 kilometers
high. After the eruption, the volcano was 2.53 kilometers high
Use the bar diagram to find the difference in height of the volcano
before and after the eruption, in meters,
2.59 km
Click the icon to see the metric units of length
meters,
The difference in height of the volcano before and after the eruption is
(Type a whole number or a decimal)
Answers
Answer:
0.4
Step-by-step explanation:
Complete the square -3x^2+12x-7
Answers
Answer:
\(-3(x-2)^2+5\)
Step-by-step explanation:
First we can factor a -3 from the \(x^2\) term and the \(x\) term to get \(-3(x^2-4x)-7\).
Then we want the stuff in the parentheses to have the form of \((x+b)^2\), or equivalently, \((x^2+2b+b^2)\) . So we can let \(2b = -4\). By solving it, we get \(b = -4/2 = -2\). Then our \(b^2\) term should be \(b^2 = (-2)^2 = 4\).
In order to make our \(b^2\) term appear in the parentheses, we need to add and subtract our \(b^2\) term, so we get \(-3(x^2 - 4x + 4 - 4) -7\).
What we to keep inside our parentheses is \((x^2 - 4x + 4)\) , so we can factor the \(-4\) out of parentheses to get \(-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5\)
Finally, plugging \(b = -2\) that we computed earlier into the equation \((x^2+2b+b^2) = (x+b)^2\), we get \((x^2 - 4x + 4) = (x-2)^2\).
So we have \(-3(x^2-4x+4)+5 = -3(x-2)^2+5\).
In summary, the procedure is
\(-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5\)
Write 0.000000624 in scientific notation
Answers
Answer:
6.24 x \(10^{-7}\)
Step-by-step explanation:
0.000000624 in scientific notation is 6.24 x \(10^{-7}\)
Answer:
Step-by-step explanation:
The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.
Find the AC
47in
14in
26in
7in
Answers
Answer: need more of an explanation
Step-by-step explanation:
Answer:
26 in.
Step-by-step explanation:
Since angles A and C are congruent, sides BC and BA are congruent.
7x - 13 = x + 29
6x = 42
x = 7
AC = 3x + 5
AC = 3(7) + 5
AC = 21 + 5
AC = 26
Answer: 26 in.
State the name of the property illustrated.
4(-8+5)= - 32 + 20
Answers
The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.
The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.
In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:
4(-8 + 5) = (4 * -8) + (4 * 5)
This simplifies to:
4(-8 + 5) = -32 + 20
Finally, we can perform the addition:
-32 + 20 = -12
Therefore, the equation demonstrates the application of the Distributive Property.
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What is the distance between point C and point D?
Question 5 options:
A)
17 units
B)
13 units
C)
12 units
D)
√85 units
Answers
Answer:
B. 13 units
Step-by-step explanation:
let
(x1 , y1) = (-4 , -6)
(x2 , y2) = (1 , 6)
distance between CD = root (x2 - x1)^3 + (y2 - y1)
= root {1 - ( -4)}^2 + {6 - ( -6)}^2
= root {1 +4}^2 + {6+6}^2
= root 5^2 + 12^2
= root 25 + 144
= root 169
= 13 units ans
Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three fives in succession from a standard deck of 52 cards with replacement, you give him $70. Otherwise, he pays you $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
Answers
The expected value of the bet, given amount you'll pay if your friend pulls three fives in succession, is $9. 99
How to find the expected value?To find the expected value, you first need to find the probability that your friend picks three fives in succession.
There are 4 fives in a standard deck of 52 cards so the probability that your friend will pick three of them in succession is:
= 4 / 52 x 3 / 51 x 2 / 50
= 1 / 5, 525
The probability that he does not get the cards is:
= 1 - 1 / 5, 525
= 5, 524 / 5, 525
The expected value of your bet is therefore:
= ( Probability that your friend pulls the three fives x Loss to you ) + ( Probability that your friend does not pull the cards x Amount you gain)
= ( 1 / 5, 525 x - 70) + (5, 524 / 5, 525 x 10 )
= $9. 99
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